Polytope of Type {24,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,3}*576
if this polytope has a name.
Group : SmallGroup(576,5053)
Rank : 3
Schlafli Type : {24,3}
Number of vertices, edges, etc : 96, 144, 12
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,3,2} of size 1152
Vertex Figure Of :
   {2,24,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {8,3}*192
   4-fold quotients : {12,3}*144
   12-fold quotients : {4,3}*48
   16-fold quotients : {6,3}*36
   24-fold quotients : {4,3}*24
   48-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,3}*1152a, {24,6}*1152a, {24,6}*1152c
   3-fold covers : {24,9}*1728, {24,3}*1728
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 2.
      8 facets:
         4 of {12}*24
         4 of {24}*48
      48 vertex figures:
         48 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2> of order 2.
      6 facets:
         6 of {24}*48
      48 vertex figures:
         48 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
      4 facets:
         2 of {12}*24
         2 of {24}*48
      24 vertex figures:
         24 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 4.
      6 facets:
         4 of {6}*12
         2 of {24}*48
      24 vertex figures:
         24 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2, s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
      4 facets:
         2 of {12}*24
         2 of {24}*48
      24 vertex figures:
         24 of {3}*6

Permutation Representation (GAP) :

s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,41)(18,42)(19,43)(20,44)(21,48)(22,47)(23,46)(24,45)(25,33)(26,34)(27,35)(28,36)(29,40)(30,39)(31,38)(32,37);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(35,36)(37,44)(38,43)(39,41)(40,42)(45,46);;
s2 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)(32,39);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,41)(18,42)(19,43)(20,44)(21,48)(22,47)(23,46)(24,45)(25,33)(26,34)(27,35)(28,36)(29,40)(30,39)(31,38)(32,37);
s1 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(35,36)(37,44)(38,43)(39,41)(40,42)(45,46);
s2 := Sym(48)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)(32,39);
poly := sub<Sym(48)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;

References : None.
to this polytope

Polytope of Type {24,3}

Twisty Puzzle